Amirmasoud Taki, Afshin Firouzi, and Saeed Mohammadzadeh



A time-dependent reliability analysis of reinforced concrete (RC) beams shear-strengthened with carbon fiber-reinforced polymer (CFRP) sheets is conducted.

Environmental effects are considered as two state degradation function representing retention in strength of CFRP and three state chloride ion attack on steel reinforcement. Modeling these deterioration mechanisms, a time-variant reliability analysis of fiber-reinforced polymer (FRP)-strengthened beams with respect to possible shear failures, including delamination of FRP sheets and ultimate shear failure, are conducted during their lifetime.

In the proposed methodology, these shear failure limit states are formulated based on the ACI 440.2R provisions; then, an event-based Monte Carlo simulation (MCS) is employed to calculate lifetime reliability indexes. The merit of the proposed reliability analysis framework is that by explicitly considering the environmental deterioration mechanisms in different harshness classifications, one can more precisely predict the lifetime risk of failure.

It is found that by using the proposed analysis framework, the probability of the survival of the beam conditional on FRP delamination can be calculated. Furthermore, this study reveals the impact of the level of load-carrying capacity of delaminated FRPs—namely, α factor—on the ultimate reliability of beams.

It is concluded that there is a significant difference of the safety of beams with the variable levels of α, which highlights the need for further investigation of the real behavior of these strengthened beams to classify into serviceability or ultimate limit state.


carbon fiber-reinforced polymer (CFRP); deterioration models; Monte Carlo simulation (MCS); reinforced concrete (RC); shear failure; time-dependent reliability analysis